Table of Contents

A Web Server for Zoomable Chaos Game Represenations

Overview

Chaos Game Representation

Chaos Game Representation (CGR) is a generalized scale-independent Markov probability table for the sequence, and oligomer tables (see document for "kmer_table" function) can be deduced from CGR image.

CGR is generated by the following procedure:

Start from position (0,0) or the origin of two dimensional coordinate.

Four nucleotides are located at the four corners:
A: (-1, 1) upper left
T: (1, -1) lower right
G: (1, 1) upper right
C: (-1, -1) lower left

For each nucleotide, move and mark the new location which is halfway between the current location and the nucleotide. For example, if the first letter is A, position is moved from (0,0) to midpoint between (-1, 1) and (0,0), which is (-0.5, 0.5).

Repeat this procedure for all nucleotides.

k-mer table

This program creates an image showing the abundance of all k-mers (oligonucleotides of length k) in a given sequence. For example, for tetramers (k=4), resulting image is composed of 4^4 = 256 boxes, each representing an oligomer. Oligomer name and abundance is written within these boxes, and abundance is also visualized with the box color, from white (none) to black (highly frequent).

This k-mer table is alternatively known as the FCGR (frequency matrices extracted from Chaos Game Representation).

Position of the oligomers can be recursively located as follows:

For each letter in an oligomer, a box is subdivided into four quadrants, where A is upper left, T is lower right, G is upper right, and C is lower left. Therefore, oligomer ATGC is in the

A = upper left quadrant
T = lower right within the above quadrant
G = upper right within the above quadrant
C = lower left within the above quadrant

In order to change the parameters, such as the length of oligomers for kmer_table (-k option), generation of Google Map (-gmap⇒1 option), or changing the image width for cgr (-width option), simply add these options and values to the function call, as follows: